Why do only high street firms want me?

I have been offered interviews at a couple of high street and small/medium law firms, but none from large City firms – what am I doing wrong?

I have held my hopes out to join a large City firm, but so far have only been offered interviews at the small and high street firms that I applied to as my back-ups. I have really good predicted grades, good a-levels and a host of extra-curricular activites on my CV – what else can I do to make myself stand out?